THE CENTERING OF THE SYSTEMS OF LENSES. 81 



The real objective-image a'" V" attains the greatest possible 

 distinctness in this special case, but since the part ~b" x of the 

 object is already indistinct, it is indistinct also in the image. 

 If, on the other hand, the displacement of the virtual image 

 is greater or less than that of the axis, a corresponding marginal 

 portion of the red image appears under less favourable conditions 

 in the first case on the left, and in the second on the right 

 side, and is, in consequence, less sharp. The part V" x is therefore 

 somewhat indistinct again at the edge. 



With every displacement, therefore, a corresponding portion of 

 the margin of the objective-image disappears, so that, in reality, 

 if the erroneous centering of the flint- and crown-lenses is also 

 taken into account, the whole periphery of the field of view must 

 suffer more or less, only a central portion is preserved in its 

 original purity, and this portion may, nevertheless, have any 

 excentric position. 



In order to obtain a few data as to the extent to which the 

 displacements represented in our figure influence the microscopic 

 image, we will assume that the first lens magnifies three linear, 

 and the second and third four and six linear respectivelv a 

 proportion which approximately coincides with actual observation. 

 The displacement of the axis o 2 would amount to '25, and 

 that of the axis o 3 to *5 mm. Therefore V x = -25, ~b" x = 1, 

 V" x = 6 mm. ; further ft" V (in a direction at right angles to 

 the axis) = (4 1) x *25 = *75 mm., and consequently a portion 

 of 6 x ('75 *5) = 1'5 mm. in breadth, measured from &'", 

 is rendered indistinct in the objective-image. This portion, 

 however, if the diaphragm in the eye-piece is supposed to be 

 immovable, falls upon its margin ; for since a" I" appears dis- 

 placed by -25 mm. further to the right than # 3 , the objective- 

 image lies, with reference to 3 , at a distance of 6 x '26 = 1'5 mm., 

 and therefore, with reference to P Q or to a" ft'", the field of 

 view of the eye-piece in the concentric system, at a distance 

 of 1 '5 -5 = 1 mm. further to the left. (In the Fig. it is 

 the reverse.) If the diameter of this field of view, i.e., of 

 the diaphragm in the eye-piece, is 18 mm., there still remain 

 5 mm. visible of the indistinct portion &'" x, while on the 

 other side, between a'" and a" ', 1 mm. of the aperture is unoc- 

 cupied, and can only be filled if the object a b is increased 

 T V mm. at a. This increase becomes somewhat less distinct in 



G 



